The results below are complete, since the LMFDB contains all isogeny classes of abelian varieties of dimension at most 2 over fields of cardinality at most 211 or 243, 256, 343, 512, 625, 729, 1024

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Results (1-50 of 2821 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.41.ay_is $2$ $\F_{41}$ $( 1 - 12 x + 41 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-5}) \) $C_2$ 1.41.am 2
2.41.ax_if $2$ $\F_{41}$ $1 - 23 x + 213 x^{2} - 943 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-17 +2 \sqrt{5}})\) $D_{4}$ simple
2.41.ax_ig $2$ $\F_{41}$ $( 1 - 12 x + 41 x^{2} )( 1 - 11 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.41.am $\times$ 1.41.al
2.41.aw_hs $2$ $\F_{41}$ $1 - 22 x + 200 x^{2} - 902 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-16 -6 \sqrt{3}})\) $D_{4}$ simple
2.41.aw_ht $2$ $\F_{41}$ $1 - 22 x + 201 x^{2} - 902 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-35 +16 \sqrt{2}})\) $D_{4}$ simple
2.41.aw_hu $2$ $\F_{41}$ $( 1 - 12 x + 41 x^{2} )( 1 - 10 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.41.am $\times$ 1.41.ak
2.41.aw_hv $2$ $\F_{41}$ $( 1 - 11 x + 41 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-43}) \) $C_2$ 1.41.al 2
2.41.av_hf $2$ $\F_{41}$ $1 - 21 x + 187 x^{2} - 861 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-26 +2 \sqrt{21}})\) $D_{4}$ simple
2.41.av_hg $2$ $\F_{41}$ $1 - 21 x + 188 x^{2} - 861 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{17})\) $C_2^2$ simple
2.41.av_hh $2$ $\F_{41}$ $1 - 21 x + 189 x^{2} - 861 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-202 +42 \sqrt{13}})\) $D_{4}$ simple
2.41.av_hi $2$ $\F_{41}$ $( 1 - 12 x + 41 x^{2} )( 1 - 9 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-83}) \) $C_2$, $C_2$ 1.41.am $\times$ 1.41.aj
2.41.av_hj $2$ $\F_{41}$ $1 - 21 x + 191 x^{2} - 861 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-210 +42 \sqrt{5}})\) $C_4$ simple
2.41.av_hk $2$ $\F_{41}$ $( 1 - 11 x + 41 x^{2} )( 1 - 10 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.41.al $\times$ 1.41.ak
2.41.au_gt $2$ $\F_{41}$ $1 - 20 x + 175 x^{2} - 820 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-57 +20 \sqrt{7}})\) $D_{4}$ simple
2.41.au_gu $2$ $\F_{41}$ $1 - 20 x + 176 x^{2} - 820 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-58 +20 \sqrt{6}})\) $D_{4}$ simple
2.41.au_gv $2$ $\F_{41}$ $1 - 20 x + 177 x^{2} - 820 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-154 +2 \sqrt{5}})\) $D_{4}$ simple
2.41.au_gw $2$ $\F_{41}$ $( 1 - 12 x + 41 x^{2} )( 1 - 8 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.41.am $\times$ 1.41.ai
2.41.au_gx $2$ $\F_{41}$ $1 - 20 x + 179 x^{2} - 820 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-61 +20 \sqrt{3}})\) $D_{4}$ simple
2.41.au_gy $2$ $\F_{41}$ $1 - 20 x + 180 x^{2} - 820 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-62 +20 \sqrt{2}})\) $D_{4}$ simple
2.41.au_gz $2$ $\F_{41}$ $( 1 - 11 x + 41 x^{2} )( 1 - 9 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-83}) \) $C_2$, $C_2$ 1.41.al $\times$ 1.41.aj
2.41.au_ha $2$ $\F_{41}$ $( 1 - 10 x + 41 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.41.ak 2
2.41.at_gg $2$ $\F_{41}$ $1 - 19 x + 162 x^{2} - 779 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-74 +2 \sqrt{41}})\) $D_{4}$ simple
2.41.at_gh $2$ $\F_{41}$ $1 - 19 x + 163 x^{2} - 779 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-258 -38 \sqrt{37}})\) $D_{4}$ simple
2.41.at_gi $2$ $\F_{41}$ $1 - 19 x + 164 x^{2} - 779 x^{3} + 1681 x^{4}$ $1$ \(\Q(\sqrt{-166 +26 \sqrt{33}})\) $D_{4}$ simple
2.41.at_gj $2$ $\F_{41}$ $1 - 19 x + 165 x^{2} - 779 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-266 -38 \sqrt{29}})\) $D_{4}$ simple
2.41.at_gk $2$ $\F_{41}$ $( 1 - 12 x + 41 x^{2} )( 1 - 7 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.41.am $\times$ 1.41.ah
2.41.at_gl $2$ $\F_{41}$ $1 - 19 x + 167 x^{2} - 779 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-274 -38 \sqrt{21}})\) $D_{4}$ simple
2.41.at_gm $2$ $\F_{41}$ $1 - 19 x + 168 x^{2} - 779 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-58 +2 \sqrt{17}})\) $D_{4}$ simple
2.41.at_gn $2$ $\F_{41}$ $1 - 19 x + 169 x^{2} - 779 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-282 -38 \sqrt{13}})\) $D_{4}$ simple
2.41.at_go $2$ $\F_{41}$ $( 1 - 11 x + 41 x^{2} )( 1 - 8 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.41.al $\times$ 1.41.ai
2.41.at_gp $2$ $\F_{41}$ $1 - 19 x + 171 x^{2} - 779 x^{3} + 1681 x^{4}$ $2$ \(\Q(\zeta_{5})\) $C_4$ simple
2.41.at_gq $2$ $\F_{41}$ $( 1 - 10 x + 41 x^{2} )( 1 - 9 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-83}) \) $C_2$, $C_2$ 1.41.ak $\times$ 1.41.aj
2.41.as_ft $2$ $\F_{41}$ $1 - 18 x + 149 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{14})\) $C_2^2$ simple
2.41.as_fu $2$ $\F_{41}$ $1 - 18 x + 150 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-34 +6 \sqrt{13}})\) $D_{4}$ simple
2.41.as_fv $2$ $\F_{41}$ $1 - 18 x + 151 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-65 +32 \sqrt{3}})\) $D_{4}$ simple
2.41.as_fw $2$ $\F_{41}$ $1 - 18 x + 152 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-8 +2 \sqrt{11}})\) $D_{4}$ simple
2.41.as_fx $2$ $\F_{41}$ $1 - 18 x + 153 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-73 -18 \sqrt{10}})\) $D_{4}$ simple
2.41.as_fy $2$ $\F_{41}$ $( 1 - 12 x + 41 x^{2} )( 1 - 6 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.41.am $\times$ 1.41.ag
2.41.as_fz $2$ $\F_{41}$ $1 - 18 x + 155 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-75 +36 \sqrt{2}})\) $D_{4}$ simple
2.41.as_ga $2$ $\F_{41}$ $1 - 18 x + 156 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-76 -18 \sqrt{7}})\) $D_{4}$ simple
2.41.as_gb $2$ $\F_{41}$ $1 - 18 x + 157 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-77 -18 \sqrt{6}})\) $D_{4}$ simple
2.41.as_gc $2$ $\F_{41}$ $1 - 18 x + 158 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-18 +3 \sqrt{5}})\) $D_{4}$ simple
2.41.as_gd $2$ $\F_{41}$ $( 1 - 11 x + 41 x^{2} )( 1 - 7 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.41.al $\times$ 1.41.ah
2.41.as_ge $2$ $\F_{41}$ $1 - 18 x + 160 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-80 -18 \sqrt{3}})\) $D_{4}$ simple
2.41.as_gf $2$ $\F_{41}$ $1 - 18 x + 161 x^{2} - 738 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-9 -2 \sqrt{2}})\) $D_{4}$ simple
2.41.as_gg $2$ $\F_{41}$ $( 1 - 10 x + 41 x^{2} )( 1 - 8 x + 41 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.41.ak $\times$ 1.41.ai
2.41.as_gh $2$ $\F_{41}$ $( 1 - 9 x + 41 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-83}) \) $C_2$ 1.41.aj 2
2.41.ar_fg $2$ $\F_{41}$ $1 - 17 x + 136 x^{2} - 697 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-18 +2 \sqrt{73}})\) $D_{4}$ simple
2.41.ar_fh $2$ $\F_{41}$ $1 - 17 x + 137 x^{2} - 697 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-298 +34 \sqrt{69}})\) $D_{4}$ simple
2.41.ar_fi $2$ $\F_{41}$ $1 - 17 x + 138 x^{2} - 697 x^{3} + 1681 x^{4}$ $2$ \(\Q(\sqrt{-302 +34 \sqrt{65}})\) $D_{4}$ simple
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